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A general control variate method for Lévy models in finance

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  • Shiraya, Kenichiro
  • Uenishi, Hiroki
  • Yamazaki, Akira

Abstract

This study proposes a new control variate method for Lévy models in finance. Our method generates a process of the control variate whose initial and terminal values coincide with those of the target Lévy model process, with both processes being driven by the same Brownian motion in the simulation. These features efficiently reduce the variance of the Monte Carlo simulation. As a typical application of this method, we provide the calculation scheme for pricing path-dependent exotic options.

Suggested Citation

  • Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:3:p:1190-1200
    DOI: 10.1016/j.ejor.2020.01.043
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    References listed on IDEAS

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    1. Shiraya, Kenichiro & Takahashi, Akihiko, 2017. "A general control variate method for multi-dimensional SDEs: An application to multi-asset options under local stochastic volatility with jumps models in finance," European Journal of Operational Research, Elsevier, vol. 258(1), pages 358-371.
    2. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.
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    10. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384, July.
    11. Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    12. Yuji Umezawa & Akira Yamazaki, 2015. "Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 133-161, April.
    13. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
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    16. Yuan Li & Kaimon Miyachi & Kenichiro Shiraya & Akira Yamazaki, 2019. "Approximation Method Using Black-Scholes Formula for Barrier Option Pricing under Lévy Models," CARF F-Series CARF-F-454, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2021.
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    Cited by:

    1. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "Efficient simulation of generalized SABR and stochastic local volatility models based on Markov chain approximations," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1046-1062.
    2. P. D. Hinds & M. V. Tretyakov, 2022. "Neural variance reduction for stochastic differential equations," Papers 2209.12885, arXiv.org, revised May 2023.
    3. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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